arXiv subjects

Ekaterina Stuken

Publications and source records attributed to Ekaterina Stuken.

3 recordsLinked to original sources

arXiv2022

Nonfreeness of some algebras of hermitian modular forms

We study the algebras of hermitian automorphic forms for the lattice $L_n=diag(1,1,\ldots,1,-1)$ and for the field $K=\mathbb{Q}(\sqrt{-d})$ such that $p=2$ is unramified and the ring of integers $\mathcal{O}_K$ is a p.i.d. We prove that for $d>7$ these algebras can't be free. When $d=7$ and $d=3$ we give an estimate for the dimension of the symmetric spaces for which these algebras might be free. We also compare our results with the known results for $d=3$.

math.NT↗

arXiv2017

Nonfreeness of algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$ where d>5

We study the algebras of symmetric Hilbert modular forms of even weight for $\mathbb{Q}(\sqrt{d})$, considering them as modular forms for the orthogonal group of the lattice with signature (2,2). Comparing the volume of the corresponding symmetric domain with the volume of the Jacobian of the generators of these algebras, we prove that for all d, except for d=2, 3, 5 these algebras can't be free.

math.NT↗

arXiv2016

Arithmetic volumes of indefinite ternary lattices with square free discriminant

The main purpose of this paper is to give an explicit formula for the volumes of indefinite ternary lattices with square free discriminant. We also consider several examples of lattices, for which the fundamental domain is well-known and make sure the results obtained by our computation coincide with the known ones.

math.NT↗